The harmonic mean of 2 numbers is 4. Their arithmetic mean A and geometric mean G satisfy the relation 2A + G2 = 27. The sum of the numbers is
Let the numbers be a & b
H = 4
G2 = AH = 4A -------------(1)
Given 2A + G2 = 27 -----------(2)
From (1) & (2)
6A = 27 ⇒ A = 92
G2 = 4 × 92 = 18
If we know A and G, the 2 numbers are given by,
a, b = A ± √A2−G2
= 92 ± √814−18
= 92 ± 32 = 6, 3 (or) 3, 6
Therefore, the sum of the numbers = 9